live-query-sample.js

Parse.Cloud.afterLiveQueryEvent('DogObject', async (request) => {
    if (request.event == "Create") {
        // If I am creating a new Dog
        const thisDog = request.object;
        thisDog.set('name', 'Fido'); // Set its name to Fido        
    } else if (request.event == "update") {
        // Else, if I am Updating an existing Dog
        const thisDog = request.object;
        thisDog.set('name', 'Rex'); // Set its name to Rex   
    } else {
        // Otherwise, do nothing
        return;
    }
});

} else if (request.event == "update") {

Related to this issue in the Parse Server repo, at the moment, request.event needs to contain a capitalized first letter. So this should be request.event == 'Update'.

   // Otherwise, do nothing
   return;

These lines here will do nothing, unless there is more below obviously, but it won't prevent the event from firing. If your intention is to do nothing on the client side too by preventing the event from firing, you can use:

    } else {
        // Otherwise, do nothing
        request.sendEvent = false;
        return;
    }